International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 3005-3013
doi:10.1155/IJMMS.2005.3005

On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c0 and c

Abstract

We determine the fine spectrum of the generalized difference operator B(r,s) defined by a band matrix over the sequence spaces c0 and c, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ, and includes as other special cases the right shift and the Zweier matrices.